GEOLOGICAL PERIODS

Q.: What exactly the criteria are for where a new geologic period starts?

There is a bit of convention and history involved.

The main criterion is whether something BIG happened, but of course the definition of big isn't absolute.

When biological traces are present, it can sometimes be rather easy to define a before/after, i.e. whether a specie, family, genus is present or not (dinosaurs, dryas), or whether red iron from oxidation caused by photosynthesis is precipitating or not. But often that level of detail is missing, more so the farther one looks back.

Look at where the "golden spikes" are sometimes ceremoniously hammered into actual rocks. For there there is a broad set of criteria to determine that something big happened and to coordinate the dating of the event in the different strata that can be found around the world.https://engineering.purdue.edu/Stratigraphy/gssp/gssp_r.html

The International Commission on Stratigraphy, an organ of the International Union of Geological Sciences, works since 1974 on identifying all the various subdivisions of geological history and on coordinating their dating worldwide.